“The swell was flash, so I could not draw his fogle.”

Let’s dissect:

Swell: gentleman (1811 Dictionary of the Vulgar Tongue by Francis Grose)

Flash: Knowing. Understanding another’s meaning.   (1891 American Slang Dictionary by James Maitland)

Draw his fogle: pick his pocket of his silk handkerchief.  (1891 American Slang Dictionary by James Maitland)

In other words: the gentleman knew exactly what I was doing so I could not sneak the silk handkerchief from his pocket.